Nonlinear Hysteretic Torsional Waves.

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.

Slow relaxation and aging phenomena at the nanoscale in granular materials.

Granular matter exhibits a rich variety of dynamic behaviors, for which the role of thermal fluctuations is usually ignored. Here we show that thermal fluctuations can pronouncedly affect contacting nanoscale asperities at grain interfaces and brightly manifest themselves through the influence on nonlinear-acoustic effects. The proposed mechanism based on intrinsic bistability of nanoscale contacts comprises a wealth of slow-dynamics regimes including slow relaxations and aging as universal properties of a wide class of systems with metastable states.

Picosecond opto-acoustic interferometry and polarimetry in high-index GaAs.

By means of a metal opto-acoustic transducer we generate quasi-longitudinal and quasi-transverse picosecond strain pulses in a (311)-GaAs substrate and monitor their propagation by picosecond acoustic interferometry. By probing at the sample side opposite to the transducer the signals related to the compressive and shear strain pulses can be separated in time. In addition to conventional monitoring of the reflected probe light intensity we monitor also the polarization rotation of the optical probe beam. This polarimetric technique results in improved sensitivity of detection and provides comprehensive information about the elasto-optical anisotropy. The experimental observations are in a good agreement with a theoretical analysis.

Vibrations of microspheres probed with ultrashort optical pulses.

We use ultrashort optical pulses to excite and detect vibrations of single silica spheres with a diameter of 5 microm placed at the surface of an acoustically mismatched substrate. In addition to the photoelastic detection of picosecond longitudinal acoustic pulses propagating inside the bulk, we detect gigahertz acoustic resonances of the sphere through probe beam defocusing. The mode frequencies are in close accord with those calculated from the elastic vibrations of a free sphere. We also record a resonant enhancement in the amplitude of specific modes of two touching spheres.

Nonlinear effects for coda-type elastic waves in stressed granular media.

Experimental results and their interpretations are presented on the nonlinear acoustic effects of multiple scattered elastic waves in unconsolidated granular media. Short wave packets with a central frequency higher than the so-called cutoff frequency of the medium are emitted at one side of the statically stressed slab of glass beads, and received at the other side after multiple-scattering and nonlinear elastic effects. Typical signals are strongly distorted compared to their initially radiated shape both due to nonlinearity and scattering. It is shown that acoustic waves with a deformation amplitude much lower than the mean static deformation of the contacts in the medium can modify the elastic properties of the medium. This addresses the problem of acoustic wave action on granular matter during and after acoustic excitation, which is necessary to understand in the nondestructive testing of the elastic properties of granular media by acoustic methods. Coda signal analysis is shown to be a powerful time-resolved tool in monitoring slight modifications in the elastic response of an unconsolidated granular structure.

Interface Adhesion and Structural Characterization of Rolled-up GaAs/In0.2Ga0.8As Multilayer Tubes by Coherent Phonon Spectroscopy.

We present a detailed experimental and theoretical study of the acoustic phonon modes in rolled-up multilayers with thickness of the layers in the nanometre and diameters in the micrometre range. We compare our results to planar, unrolled multilayers grown by molecular beam epitaxy. For the planar multilayers the experimentally obtained acoustic modes exhibit properties of a superlattice and match well to calculations obtained by the Rytov model. The rolled-up superlattice tubes show intriguing differences compared to the planar structures which can be attributed to the imperfect adhesion between individual tube windings. A transfer matrix method including a massless spring accounting for the imperfect adhesion between the layers yields good agreement between experiment and calculations for up to five windings. Areas with sufficient mechanical coupling between all windings can be distinguished by their acoustic mode spectrum from areas where individual windings are only partially in contact. This allows the spatially resolved characterization of individual tubes with micrometre spatial resolution where areas with varying interface adhesion can be identified.

Surface waves in granular phononic crystals.

The existence of surface elastic waves at a mechanically free surface of granular phononic crystals is studied. The granular phononic crystals are made of spherical particles distributed periodically on a simple cubic lattice. It is assumed that the particles are interacting by means of normal, shear, and bending contact rigidities. First, Rayleigh-type surface acoustic waves, where the displacement of the particles takes place in the sagittal plane while the particles possess one rotational and two translational degrees of freedom, are analyzed. Second, shear-horizontal-type waves, where the displacement of the particles is normal to the sagittal plane while the particles possess one translational and two rotational degrees of freedom are studied. The existence of zero-group-velocity surface acoustic waves of Rayleigh type is theoretically predicted and interpreted. A comparison with surface waves predicted by the reduced Cosserat theory is performed, and some limitations of the latter are established.

Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes.

Self-action and effects mutually induced by oscillations interacting in hysteretic media are investigated analytically and numerically. Special attention is paid to non-simplex processes for which presence of intermediate extrema results in appearance of minor nested loops inside the main hysteretic stress-strain loop. Non-simplex regimes are typical of interaction of excitations having different frequencies and amplitudes, but comparable strain rates. It is found that, due to transition between the regimes, frequency and amplitude dependencies of the variations in elasticity and dissipation induced by one wave for another one may become non-monotonous. Either additional dissipation or induced transparency may occur in different regimes. The results obtained are important for correct interpretation of experimental data on nonlinear acoustic interactions in rocks and many other microstructured (mesoscopic) solids that are known to exhibit elastic hysteresis and memory properties.

Self-demodulation of elastic waves in a one-dimensional granular chain.

The self-demodulation process in a nonlinear granular chain of identical beads is studied analytically and numerically. In such a medium, in accordance with the dispersion relation, longitudinal waves that have a frequency higher than the so-called cutoff frequency of the chain are evanescent. Here, we study the influence on the self-demodulation process of the transition from the propagative to the evanescent regime in pump wave propagation that takes place when the pump frequency increases. An analytical solution in discrete coordinates is derived for the case of two primary frequencies mixing into a single difference frequency. This solution is then numerically integrated in order to analyze the demodulation of the acoustic wave packet (i.e., of the harmonic acoustic wave modulated in a pulse mode). Temporal demodulated profiles can be strongly sensitive to the regime (propagative or evanescent) of primary wave transport. This model allows us to detect the cutoff frequency of longitudinal elastic waves in the chain, without receiving the primary waves, but receiving the low frequency nonlinearly radiated signal. The roles of frequency dependent attenuation, velocity dispersion, and observation distance are analyzed.

Influence of ballistics to diffusion transition in primary wave propagation on parametric antenna operation in granular media.

A model of parametric transmitting antenna in granular media is developed, which takes into account velocity dispersion, frequency-dependent absorption, and frequency-dependent scattering of acoustic waves in granular media. The latter process may induce a transition from the ballistics to the diffusion regime of pump (primary) high-frequency wave propagation with increasing frequency. The conditions under which the transition from ballistics to diffusion manifests itself in the change of the demodulated (rectified) low-frequency acoustic pulse profile are established. It is demonstrated that parametric low-frequency radiation contains information on both absorption and scattering of high-frequency acoustic waves.

Evolution equation for nonlinear Scholte waves.

The evolution equations for nonlinear Scholte waves (finite amplitude elastic waves propagating along liquid/solid interface), which account for the second order nonlinearity of a liquid, are derived for the first time. For mathematical simplicity the nonlinearity of the solid, which influence is expected to be weak in the case of weak localization of the Scholte wave, is not taken into consideration. The analysis of these equations demonstrates that the nonlinear processes contributing to the evolution of the Scholte wave can be divided into two groups. The first group includes nonlinear processes leading to wave spectrum broadening which are common to bulk pressure waves in liquids and gases. The second group includes the nonlinear processes which are active only in the frequency down-conversion (leading to wave spectrum conservation or narrowing), which are specific to the confined nature of the interface wave. It is demonstrated that the nonlinear parameters, which characterize the efficiency of various nonlinear processes in the interface wave, strongly depend on the relative properties of the contacting liquid and solid (or, in other words, on the deviation of the Scholte wave velocity from the velocities of sound in liquid and in solid). In particular, the sign of the nonlinear parameter responsible for the second harmonic generation can differ from the sign of the nonlinear acoustic parameter of the liquid. It is also verified that there are particular liquid/solid combinations where the nonlinear processes, which are inactive in the frequency up-conversion, dominate in the evolution of the Scholte wave. In this case distortionless propagation of the finite amplitude harmonic interface wave is possible. The proposed theory should find applications in nonlinear acoustics, geophysics, and nondestructive testing.

Spatiotemporal mapping of surface acoustic waves in isotropic and anisotropic materials.

We demonstrate a new method for a real-time imaging of surface acoustic waves at frequencies up to 1 GHz with picosecond temporal and micron spatial resolutions using an ultrafast optical pump and probe technique combined with a common path interferometer. Using samples with isotropic or anisotropic substrates coated with metallic thin films, we observe the propagation of Rayleigh-like modes and surface-skimming bulk modes as well as resolving surface phonon focusing effects. In addition we image surface acoustic wave propagation in a laterally inhomogeneous sample.

Localized transversal-rotational modes in linear chains of equal masses.

The propagation and localization of transversal-rotational waves in a two-dimensional granular chain of equal masses are analyzed in this study. The masses are infinitely long cylinders possessing one translational and one rotational degree of freedom. Two dispersive propagating modes are predicted in this granular crystal. By considering the semi-infinite chain with a boundary condition applied at its beginning, the analytical study demonstrates the existence of localized modes, each mode composed of two evanescent modes. Their existence, position (either in the gap between the propagating modes or in the gap above the upper propagating mode), and structure of spatial localization are analyzed as a function of the relative strength of the shear and bending interparticle interactions and for different boundary conditions. This demonstrates the existence of a localized mode in a semi-infinite monatomic chain when transversal-rotational waves are considered, while it is well known that these types of modes do not exist when longitudinal waves are considered.

Second-harmonic generation for dispersive elastic waves in a discrete granular chain.

The propagation of nonlinear compressional waves in a one-dimensional granular chain driven at one end by a harmonic excitation is studied. The chain is described by a Fermi-Pasta-Ulam (FPU) lattice model with quadratic nonlinearity (α-FPU model), valid for strong initial compression of the chain by an external static force. A successive approximations method is used to obtain the analytical expressions for the amplitudes of the static displacement field and of the fundamental and second harmonics propagating through the lattice. Both propagating and evanescent second harmonics are shown to influence the nonlinear propagation characteristics of the fundamental frequency. The propagating regime is characterized by a periodic energy transfer between first and second harmonics, resulting from dispersion, which disappears when the second harmonic becomes evanescent.

Acoustic probing of the jamming transition in an unconsolidated granular medium.

Experimentally determined dispersion relations for acoustic waves guided along the mechanically free surface of an unconsolidated granular packed structure provide information on the elasticity of granular media at very low pressures that are naturally controlled by the gravitational acceleration and the depth beneath the surface. The experiments confirm recent theoretical predictions that relaxation of the disordered granular packing through nonaffine motion leads to a peculiar scaling of shear rigidity with pressure near the jamming transition corresponding to zero pressure.

Acoustic waves in an elastic channel near the free surface of granular media.

A theoretical description of a natural acoustical waveguide existing in unconsolidated granular materials due to a gravity-induced stiffness gradient is proposed. The analytical theory for the acoustic modes propagating in the medium with a power-law type inhomogeneity uses some original solutions of the Helmholtz equation that have not been derived before either in classical or in quantum mechanics. The dispersion relations and a physical mechanism of localization for these modes indicate their essential difference both from the Rayleigh surface acoustic waves and the waveguide modes in homogeneous plates.

Coherent shear phonon generation and detection with ultrashort optical pulses.

Using an optical technique we generate and detect picosecond shear and quasishear coherent acoustic phonon pulses in the time domain. Thermoelastic and piezoelectric generation are directly achieved by breaking the sample lateral symmetry using crystalline anisotropy. We demonstrate efficient detection in isotropic and anisotropic media with various optical incidence geometries.

Watching ripples on crystals.

We present a new method for imaging surface phonon focusing and dispersion at frequencies up to 1 GHz that makes use of ultrafast optical excitation and detection. Animations of coherent surface phonon wave packets emanating from a point source on isotropic and anisotropic solids are obtained with micron lateral resolution. We resolve rounded-square shaped wave fronts on the (100) plane of LiF and discover isolated pockets of pseudosurface wave propagation with exceptionally high group velocity in the (001) plane of TeO(2). Surface phonon refraction and concentration in a minute gold pyramid is also revealed.

Femtosecond optical nonlinearity of metallic indium across the solid liquid transition.

A very strong (~10(-8) esu) femtosecond cubic nonlinearity in metallic indium that increased sharply in magnitude as the temperature approached the melting point was observed.

Cubic optical nonlinearity of free electrons in bulk gold.

A fast (Tau(response) <90 fs) free-electron spin-f lipping frequency-degenerate nonlinearity with a signif icant value of|chi((3))(xxyy)(omega,omega,omega,-omega)chi((3))(xxyy)(omega,omega,omega,-omega)|~10(-)(8)esu has been observed in bulk gold at 1260 nm by use of a new pump-probe polarization-sensitive technique.